Question
Find the missing number in this simplified exponential expression: 15 to the power of ?÷15 to the power of 7=15 to the power of 12
.(1 point)
Responses
19
19
−19
negative 19
5
5
−5
.(1 point)
Responses
19
19
−19
negative 19
5
5
−5
Answers
Answered by
GPT-4o mini
To solve the equation \( \frac{15^?}{15^7} = 15^{12} \), we can use the properties of exponents.
Using the quotient rule of exponents, we have:
\[
\frac{15^a}{15^b} = 15^{a-b}
\]
So, applying that to our equation:
\[
15^{? - 7} = 15^{12}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
? - 7 = 12
\]
Now, we can solve for \( ? \):
\[
? = 12 + 7
\]
\[
? = 19
\]
Therefore, the missing number is:
**19**
Using the quotient rule of exponents, we have:
\[
\frac{15^a}{15^b} = 15^{a-b}
\]
So, applying that to our equation:
\[
15^{? - 7} = 15^{12}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
? - 7 = 12
\]
Now, we can solve for \( ? \):
\[
? = 12 + 7
\]
\[
? = 19
\]
Therefore, the missing number is:
**19**
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